Subject: General Aptitude · Chapter: Problems on Numbers · Exam: · Marks: · Difficulty:
If $2 \frac{1}{2}$ is added to a number and the sum multiplied by $4 \frac{1}{2}$ and 3 is added to the product and the sum is divided by $1 \frac{1}{5}$, the quotient becomes 25. What is the number?
(a)$2 \frac{1}{2}$
(b)$3 \frac{1}{2}$
(c)$4 \frac{1}{2}$
(d)$5 \frac{1}{2}$
Answer
Answer (as printed): B
Explanation
Let the number be $x$. Then, $$\frac{4 \frac{1}{2}\left(x+2 \frac{1}{2}\right)+3}{1 \frac{1}{5}}=25 \Leftrightarrow \frac{\frac{9}{2}\left(x+\frac{5}{2}\right)+3}{\frac{6}{5}}=25 \begin{aligned} & \Leftrightarrow \frac{9 x}{2}+\frac{45}{4}+3=25 \times \frac{6}{5}=30 \\ & \Leftrightarrow \frac{9 x}{2}=30-\frac{57}{4} \Leftrightarrow \frac{9 x}{2}=\frac{63}{4} \\ & \Leftrightarrow x=\left(\frac{63}{4} \times \frac{2}{9}\right)=\frac{7}{2}=3 \frac{1}{2} \end{aligned}$$
Explanation as extracted from the printed page; notation may be imperfect.